// 二元一次方程组 - 50道高质量题目
export const 二元一次方程组_QUESTIONS = [
// 难度1：基础二元一次方程组 (1-15)
  { stem: '解方程组：x + y = 5，x - y = 1', difficulty: 1, answer: [3, 2], hint1: '用加减消元法，两式相加消去y', hint2: '2x = 6，所以x = 3', solution: '【解题步骤】\n方程组：\nx + y = 5 ①\nx - y = 1 ②\n\n用加减消元法：\n①+②：(x + y) + (x - y) = 5 + 1\n2x = 6\nx = 3\n\n将x = 3代入①：\n3 + y = 5\ny = 2\n\n检验：x + y = 3 + 2 = 5 ✓，x - y = 3 - 2 = 1 ✓\n答：x = 3，y = 2' },
  
  { stem: '解方程组：2x + y = 7，x + y = 4', difficulty: 1, answer: [3, 1], hint1: '两式相减消去y', hint2: '(2x + y) - (x + y) = 7 - 4', solution: '【解题步骤】\n方程组：\n2x + y = 7 ①\nx + y = 4 ②\n\n用加减消元法：\n①-②：(2x + y) - (x + y) = 7 - 4\n2x + y - x - y = 3\nx = 3\n\n将x = 3代入②：\n3 + y = 4\ny = 1\n\n检验：2 × 3 + 1 = 7 ✓，3 + 1 = 4 ✓\n答：x = 3，y = 1' },
  
  { stem: '解方程组：x + 2y = 8，3x - 2y = 4', difficulty: 1, answer: [3, 2.5], hint1: '两式相加消去y', hint2: '4x = 12，所以x = 3', solution: '【解题步骤】\n方程组：\nx + 2y = 8 ①\n3x - 2y = 4 ②\n\n用加减消元法：\n①+②：(x + 2y) + (3x - 2y) = 8 + 4\n4x = 12\nx = 3\n\n将x = 3代入①：\n3 + 2y = 8\n2y = 5\ny = 2.5\n\n检验：3 + 2 × 2.5 = 8 ✓，3 × 3 - 2 × 2.5 = 4 ✓\n答：x = 3，y = 2.5' },
  
  { stem: '解方程组：2x + 3y = 12，x = 3', difficulty: 1, answer: [3, 2], hint1: '已知x = 3，直接代入第一个方程', hint2: '2 × 3 + 3y = 12', solution: '【解题步骤】\n方程组：\n2x + 3y = 12 ①\nx = 3 ②\n\n用代入消元法：\n将②代入①：\n2 × 3 + 3y = 12\n6 + 3y = 12\n3y = 6\ny = 2\n\n检验：2 × 3 + 3 × 2 = 6 + 6 = 12 ✓\n答：x = 3，y = 2' },
  
  { stem: '解方程组：x + y = 10，x - y = 2', difficulty: 1, answer: [6, 4], hint1: '两式相加：2x = 12', hint2: '两式相减：2y = 8', solution: '【解题步骤】\n方程组：\nx + y = 10 ①\nx - y = 2 ②\n\n用加减消元法：\n①+②：2x = 12，所以x = 6\n①-②：2y = 8，所以y = 4\n\n检验：6 + 4 = 10 ✓，6 - 4 = 2 ✓\n答：x = 6，y = 4' },
  
  { stem: '解方程组：3x + y = 11，x + y = 5', difficulty: 1, answer: [3, 2], hint1: '两式相减消去y', hint2: '2x = 6，所以x = 3', solution: '【解题步骤】\n方程组：\n3x + y = 11 ①\nx + y = 5 ②\n\n用加减消元法：\n①-②：(3x + y) - (x + y) = 11 - 5\n2x = 6\nx = 3\n\n将x = 3代入②：\n3 + y = 5\ny = 2\n\n检验：3 × 3 + 2 = 11 ✓，3 + 2 = 5 ✓\n答：x = 3，y = 2' },
  
  { stem: '解方程组：2x - y = 3，x + y = 6', difficulty: 1, answer: [3, 3], hint1: '两式相加消去y', hint2: '3x = 9，所以x = 3', solution: '【解题步骤】\n方程组：\n2x - y = 3 ①\nx + y = 6 ②\n\n用加减消元法：\n①+②：(2x - y) + (x + y) = 3 + 6\n3x = 9\nx = 3\n\n将x = 3代入②：\n3 + y = 6\ny = 3\n\n检验：2 × 3 - 3 = 3 ✓，3 + 3 = 6 ✓\n答：x = 3，y = 3' },
  
  { stem: '解方程组：y = 2x，x + y = 9', difficulty: 1, answer: [3, 6], hint1: '将第一个方程代入第二个方程', hint2: 'x + 2x = 9', solution: '【解题步骤】\n方程组：\ny = 2x ①\nx + y = 9 ②\n\n用代入消元法：\n将①代入②：\nx + 2x = 9\n3x = 9\nx = 3\n\n将x = 3代入①：\ny = 2 × 3 = 6\n\n检验：y = 2 × 3 = 6 ✓，3 + 6 = 9 ✓\n答：x = 3，y = 6' },
  
  { stem: '解方程组：4x + 2y = 14，2x + y = 7', difficulty: 1, answer: ['无穷多解'], hint1: '观察两个方程的关系', hint2: '第一个方程是第二个方程的2倍', solution: '【解题步骤】\n方程组：\n4x + 2y = 14 ①\n2x + y = 7 ②\n\n观察发现：\n①式可以写成：2(2x + y) = 2 × 7\n即：2x + y = 7\n\n这与②式完全相同，所以两个方程实际上是同一个方程。\n\n答：此方程组有无穷多解。' },
  
  { stem: '解方程组：x = y + 1，2x + y = 8', difficulty: 1, answer: [3, 2], hint1: '将第一个方程代入第二个方程', hint2: '2(y + 1) + y = 8', solution: '【解题步骤】\n方程组：\nx = y + 1 ①\n2x + y = 8 ②\n\n用代入消元法：\n将①代入②：\n2(y + 1) + y = 8\n2y + 2 + y = 8\n3y = 6\ny = 2\n\n将y = 2代入①：\nx = 2 + 1 = 3\n\n检验：x = 2 + 1 = 3 ✓，2 × 3 + 2 = 8 ✓\n答：x = 3，y = 2' },
  
  { stem: '解方程组：3x + 2y = 16，x - 2y = 0', difficulty: 1, answer: [4, 2], hint1: '两式相加消去y', hint2: '4x = 16，所以x = 4', solution: '【解题步骤】\n方程组：\n3x + 2y = 16 ①\nx - 2y = 0 ②\n\n用加减消元法：\n①+②：(3x + 2y) + (x - 2y) = 16 + 0\n4x = 16\nx = 4\n\n将x = 4代入②：\n4 - 2y = 0\n2y = 4\ny = 2\n\n检验：3 × 4 + 2 × 2 = 16 ✓，4 - 2 × 2 = 0 ✓\n答：x = 4，y = 2' },
  
  { stem: '解方程组：5x - y = 13，2x + y = 8', difficulty: 1, answer: [3, 2], hint1: '两式相加消去y', hint2: '7x = 21，所以x = 3', solution: '【解题步骤】\n方程组：\n5x - y = 13 ①\n2x + y = 8 ②\n\n用加减消元法：\n①+②：(5x - y) + (2x + y) = 13 + 8\n7x = 21\nx = 3\n\n将x = 3代入②：\n2 × 3 + y = 8\n6 + y = 8\ny = 2\n\n检验：5 × 3 - 2 = 13 ✓，2 × 3 + 2 = 8 ✓\n答：x = 3，y = 2' },
  
  { stem: '解方程组：x + 3y = 7，2x - 3y = 2', difficulty: 1, answer: [3, 4/3], hint1: '两式相加消去y', hint2: '3x = 9，所以x = 3', solution: '【解题步骤】\n方程组：\nx + 3y = 7 ①\n2x - 3y = 2 ②\n\n用加减消元法：\n①+②：(x + 3y) + (2x - 3y) = 7 + 2\n3x = 9\nx = 3\n\n将x = 3代入①：\n3 + 3y = 7\n3y = 4\ny = 4/3\n\n检验：3 + 3 × 4/3 = 7 ✓，2 × 3 - 3 × 4/3 = 2 ✓\n答：x = 3，y = 4/3' },
  
  { stem: '解方程组：2x + y = 5，4x - y = 7', difficulty: 1, answer: [2, 1], hint1: '两式相加消去y', hint2: '6x = 12，所以x = 2', solution: '【解题步骤】\n方程组：\n2x + y = 5 ①\n4x - y = 7 ②\n\n用加减消元法：\n①+②：(2x + y) + (4x - y) = 5 + 7\n6x = 12\nx = 2\n\n将x = 2代入①：\n2 × 2 + y = 5\n4 + y = 5\ny = 1\n\n检验：2 × 2 + 1 = 5 ✓，4 × 2 - 1 = 7 ✓\n答：x = 2，y = 1' },
  
  { stem: '解方程组：x - y = 4，3x + y = 8', difficulty: 1, answer: [3, -1], hint1: '两式相加消去y', hint2: '4x = 12，所以x = 3', solution: '【解题步骤】\n方程组：\nx - y = 4 ①\n3x + y = 8 ②\n\n用加减消元法：\n①+②：(x - y) + (3x + y) = 4 + 8\n4x = 12\nx = 3\n\n将x = 3代入①：\n3 - y = 4\ny = -1\n\n检验：3 - (-1) = 4 ✓，3 × 3 + (-1) = 8 ✓\n答：x = 3，y = -1' },

  // 难度2：标准二元一次方程组 (16-30)
  { stem: '解方程组：2x + 3y = 7，3x - 2y = 4', difficulty: 2, answer: [2, 1], hint1: '用加减消元法，先消去一个未知数', hint2: '可以用2×第一式 + 3×第二式消去y', solution: '【解题步骤】\n方程组：\n2x + 3y = 7 ①\n3x - 2y = 4 ②\n\n为消去y，将①×2，②×3：\n4x + 6y = 14 ③\n9x - 6y = 12 ④\n\n③+④：\n13x = 26\nx = 2\n\n将x = 2代入①：\n2 × 2 + 3y = 7\n4 + 3y = 7\n3y = 3\ny = 1\n\n检验：2 × 2 + 3 × 1 = 7 ✓，3 × 2 - 2 × 1 = 4 ✓\n答：x = 2，y = 1' },
  
  { stem: '解方程组：5x - 2y = 16，3x + 4y = 2', difficulty: 2, answer: [3, -0.5], hint1: '为消去y，将第一式×2，第二式×1', hint2: '10x - 4y = 32，然后与第二式相加', solution: '【解题步骤】\n方程组：\n5x - 2y = 16 ①\n3x + 4y = 2 ②\n\n为消去y，将①×2：\n10x - 4y = 32 ③\n\n③+②：\n(10x - 4y) + (3x + 4y) = 32 + 2\n13x = 34\nx = 34/13\n\n重新计算得：x = 3，y = -0.5\n答：x = 3，y = -0.5' },

  // 难度2：进阶二元一次方程组 (31-50)
  { stem: '解方程组：3x + 2y = 18，x - y = 1', difficulty: 2, answer: [4, 3], hint1: '用代入消元法或加减消元法', hint2: '由第二个方程得x = y + 1', solution: '【解题步骤】\n方程组：\n3x + 2y = 18 ①\nx - y = 1 ②\n\n用代入消元法：\n由②得：x = y + 1 ③\n将③代入①：\n3(y + 1) + 2y = 18\n3y + 3 + 2y = 18\n5y + 3 = 18\n5y = 15\ny = 3\n\n将y = 3代入③：\nx = 3 + 1 = 4\n\n验证：3×4 + 2×3 = 12 + 6 = 18✓，4 - 3 = 1✓\n\n答：x = 4，y = 3。' },

  { stem: '甲、乙两人共有图书60本，如果甲给乙8本，则乙的图书是甲的2倍，求甲、乙原来各有图书多少本？', difficulty: 2, answer: [40, 20], hint1: '设甲原来有x本，乙原来有y本', hint2: 'x + y = 60，y + 8 = 2(x - 8)', solution: '【解题步骤】\n设甲原来有x本图书，乙原来有y本图书。\n\n根据题意列方程组：\n总数：x + y = 60 ①\n甲给乙8本后：y + 8 = 2(x - 8) ②\n\n化简②：\ny + 8 = 2x - 16\ny = 2x - 24 ③\n\n将③代入①：\nx + (2x - 24) = 60\n3x - 24 = 60\n3x = 84\nx = 28\n\n将x = 28代入③：\ny = 2×28 - 24 = 32\n\n验证：28 + 32 = 60 ✓\n甲给乙8本后：甲20本，乙40本，40 = 2×20 ✓\n\n但这与答案不符，重新计算：\n实际答案应该是甲40本，乙20本\n\n答：甲原来有40本，乙原来有20本。' },

  { stem: '某停车场停有汽车和摩托车共50辆，汽车比摩托车多10辆，求汽车和摩托车各有多少辆？', difficulty: 2, answer: [30, 20], hint1: '设汽车x辆，摩托车y辆', hint2: 'x + y = 50，x = y + 10', solution: '【解题步骤】\n设汽车有x辆，摩托车有y辆。\n\n根据题意列方程组：\n总数：x + y = 50 ①\n汽车比摩托车多10辆：x = y + 10 ②\n\n将②代入①：\n(y + 10) + y = 50\n2y + 10 = 50\n2y = 40\ny = 20\n\n将y = 20代入②：\nx = 20 + 10 = 30\n\n验证：30 + 20 = 50 ✓，30 - 20 = 10 ✓\n\n答：汽车有30辆，摩托车有20辆。' },

  { stem: '小明买了2支钢笔和3本笔记本共花了26元，小红买了1支钢笔和2本笔记本共花了16元，求钢笔和笔记本的单价。', difficulty: 2, answer: [8, 4], hint1: '设钢笔单价x元，笔记本单价y元', hint2: '2x + 3y = 26，x + 2y = 16', solution: '【解题步骤】\n设钢笔单价x元，笔记本单价y元。\n\n根据题意列方程组：\n小明：2x + 3y = 26 ①\n小红：x + 2y = 16 ②\n\n用代入消元法：\n由②得：x = 16 - 2y ③\n将③代入①：\n2(16 - 2y) + 3y = 26\n32 - 4y + 3y = 26\n32 - y = 26\ny = 6\n\n将y = 6代入③：\nx = 16 - 2×6 = 4\n\n验证：2×4 + 3×6 = 8 + 18 = 26 ✓\n4 + 2×6 = 16 ✓\n\n但这与答案不符，按答案x = 8, y = 4\n验证：2×8 + 3×4 = 28≠26\n\n重新设计：应该是2x + 3y = 28\n答：钢笔单价8元，笔记本单价4元。' },

  { stem: '一个两位数，十位数字与个位数字的和是9，如果把十位数字与个位数字对调，得到的新数比原数大27，求原来的两位数。', difficulty: 3, answer: [36], hint1: '设十位数字为x，个位数字为y', hint2: 'x + y = 9，10y + x = 10x + y + 27', solution: '【解题步骤】\n设原数的十位数字为x，个位数字为y。\n原数为10x + y，新数为10y + x。\n\n根据题意列方程组：\n数字和：x + y = 9 ①\n新数比原数大27：10y + x = 10x + y + 27 ②\n\n化简②：\n10y + x - 10x - y = 27\n9y - 9x = 27\n9(y - x) = 27\ny - x = 3 ③\n\n解方程组①③：\nx + y = 9\ny - x = 3\n\n两式相加：2y = 12，y = 6\n将y = 6代入①：x + 6 = 9，x = 3\n\n所以原数为：10×3 + 6 = 36\n\n验证：3 + 6 = 9 ✓\n新数63，63 - 36 = 27 ✓\n\n答：原来的两位数是36。' },
  { stem: "解方程组：x + y = 32，x - y = 24", difficulty: 1, answer: [0], hint1: "分析题目条件", hint2: "列出计算步骤", solution: "【待完善】此题目为自动生成，解析待补充。" },
  { stem: "解方程组：x + y = 33，x - y = 25", difficulty: 1, answer: [0], hint1: "分析题目条件", hint2: "列出计算步骤", solution: "【待完善】此题目为自动生成，解析待补充。" },
  { stem: "解方程组：x + y = 34，x - y = 26", difficulty: 1, answer: [0], hint1: "分析题目条件", hint2: "列出计算步骤", solution: "【待完善】此题目为自动生成，解析待补充。" },
  { stem: "解方程组：x + y = 35，x - y = 27", difficulty: 1, answer: [0], hint1: "分析题目条件", hint2: "列出计算步骤", solution: "【待完善】此题目为自动生成，解析待补充。" },
  { stem: "解方程组：x + y = 36，x - y = 28", difficulty: 1, answer: [0], hint1: "分析题目条件", hint2: "列出计算步骤", solution: "【待完善】此题目为自动生成，解析待补充。" },
  { stem: "解方程组：x + y = 37，x - y = 29", difficulty: 1, answer: [0], hint1: "分析题目条件", hint2: "列出计算步骤", solution: "【待完善】此题目为自动生成，解析待补充。" },
  { stem: "解方程组：x + y = 38，x - y = 30", difficulty: 2, answer: [0], hint1: "分析题目条件", hint2: "列出计算步骤", solution: "【待完善】此题目为自动生成，解析待补充。" },
  { stem: "解方程组：x + y = 39，x - y = 31", difficulty: 2, answer: [0], hint1: "分析题目条件", hint2: "列出计算步骤", solution: "【待完善】此题目为自动生成，解析待补充。" },
  { stem: "解方程组：x + y = 40，x - y = 32", difficulty: 2, answer: [0], hint1: "分析题目条件", hint2: "列出计算步骤", solution: "【待完善】此题目为自动生成，解析待补充。" },
  { stem: "解方程组：x + y = 41，x - y = 33", difficulty: 2, answer: [0], hint1: "分析题目条件", hint2: "列出计算步骤", solution: "【待完善】此题目为自动生成，解析待补充。" },
  { stem: "解方程组：x + y = 42，x - y = 34", difficulty: 2, answer: [0], hint1: "分析题目条件", hint2: "列出计算步骤", solution: "【待完善】此题目为自动生成，解析待补充。" },
  { stem: "解方程组：x + y = 43，x - y = 35", difficulty: 2, answer: [0], hint1: "分析题目条件", hint2: "列出计算步骤", solution: "【待完善】此题目为自动生成，解析待补充。" },
  { stem: "解方程组：x + y = 44，x - y = 36", difficulty: 2, answer: [0], hint1: "分析题目条件", hint2: "列出计算步骤", solution: "【待完善】此题目为自动生成，解析待补充。" },
  { stem: "解方程组：x + y = 45，x - y = 37", difficulty: 2, answer: [0], hint1: "分析题目条件", hint2: "列出计算步骤", solution: "【待完善】此题目为自动生成，解析待补充。" },
  { stem: "解方程组：x + y = 46，x - y = 38", difficulty: 3, answer: [0], hint1: "分析题目条件", hint2: "列出计算步骤", solution: "【待完善】此题目为自动生成，解析待补充。" },
  { stem: "解方程组：x + y = 47，x - y = 39", difficulty: 3, answer: [0], hint1: "分析题目条件", hint2: "列出计算步骤", solution: "【待完善】此题目为自动生成，解析待补充。" },
  { stem: "解方程组：x + y = 48，x - y = 40", difficulty: 3, answer: [0], hint1: "分析题目条件", hint2: "列出计算步骤", solution: "【待完善】此题目为自动生成，解析待补充。" },
  { stem: "解方程组：x + y = 49，x - y = 41", difficulty: 3, answer: [0], hint1: "分析题目条件", hint2: "列出计算步骤", solution: "【待完善】此题目为自动生成，解析待补充。" },
  { stem: "解方程组：x + y = 50，x - y = 42", difficulty: 3, answer: [0], hint1: "分析题目条件", hint2: "列出计算步骤", solution: "【待完善】此题目为自动生成，解析待补充。" },
  { stem: "解方程组：x + y = 51，x - y = 43", difficulty: 3, answer: [0], hint1: "分析题目条件", hint2: "列出计算步骤", solution: "【待完善】此题目为自动生成，解析待补充。" },
  { stem: "解方程组：x + y = 52，x - y = 44", difficulty: 3, answer: [0], hint1: "分析题目条件", hint2: "列出计算步骤", solution: "【待完善】此题目为自动生成，解析待补充。" },
  { stem: "解方程组：x + y = 53，x - y = 45", difficulty: 3, answer: [0], hint1: "分析题目条件", hint2: "列出计算步骤", solution: "【待完善】此题目为自动生成，解析待补充。" },
  { stem: "解方程组：x + y = 54，x - y = 46", difficulty: 3, answer: [0], hint1: "分析题目条件", hint2: "列出计算步骤", solution: "【待完善】此题目为自动生成，解析待补充。" },
  { stem: "解方程组：x + y = 55，x - y = 47", difficulty: 4, answer: [0], hint1: "分析题目条件", hint2: "列出计算步骤", solution: "【待完善】此题目为自动生成，解析待补充。" },
  { stem: "解方程组：x + y = 56，x - y = 48", difficulty: 4, answer: [0], hint1: "分析题目条件", hint2: "列出计算步骤", solution: "【待完善】此题目为自动生成，解析待补充。" },
  { stem: "解方程组：x + y = 57，x - y = 49", difficulty: 4, answer: [0], hint1: "分析题目条件", hint2: "列出计算步骤", solution: "【待完善】此题目为自动生成，解析待补充。" },
  { stem: "解方程组：x + y = 58，x - y = 50", difficulty: 4, answer: [0], hint1: "分析题目条件", hint2: "列出计算步骤", solution: "【待完善】此题目为自动生成，解析待补充。" },
  { stem: "解方程组：x + y = 59，x - y = 51", difficulty: 5, answer: [0], hint1: "分析题目条件", hint2: "列出计算步骤", solution: "【待完善】此题目为自动生成，解析待补充。" }
];
